Nine $2000, 9% bonds with interest payable semi-annually and redeemable at par are purchased 7 years before maturity. Find the premium or discount and the purchase price if the bonds are bought to yield 4%.

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The purchase price of a bond is the present value of its future cash flows, which include interest payments and the redemption value at maturity. The interest payment per bond per period is $90 (9% of $2000, paid semi-annually), and there are 14 periods remaining (7 years * 2). The redemption value is $2000 per bond. The yield per period is 2% (4% annual yield, compounded semi-annually).1. Calculate the present value of the interest payments (an annuity):$$ PV_{interest} = P \times \frac{1 - (1 + r)^{-n}}{r} $$$$ PV_{interest} = 90 \times \frac{1 - (1 + 0.02)^{-14}}{0.02} $$$$ PV_{interest} = 90 \times 11.92456684 $$$$ PV_{interest} = 1073.210018 $$2. Calculate the present value of the redemption value:$$ PV_{redemption} = F \times (1 + r)^{-n} $$$$ PV_{redemption} = 2000 \times (1 + 0.02)^{-14} $$$$ PV_{redemption} = 2000 \times 0.743157 $$$$ PV_{redemption} = 1486.314 $$3. Sum the present values for the total price per bond:$$ PV_{total} = PV_{interest} + PV_{redemption} $$$$ PV_{total} = 1073.210018 + 1486.314 $$$$ PV_{total} = 2559.524018 $$4. Calculate the total purchase price for nine bonds:$$ Total = PV_{total} \times 9 $$$$ Total = 2559.524018 \times 9 $$$$ Total = 23035.71616 $$5. Calculate the premium:Since the bonds are redeemable at par ($2000 per bond), the par value for nine bonds is $18000. The purchase price is $23035.71616, so the premium is the difference:$$ Premium = 23035.71616 - 18000 $$$$ Premium = 5035.71616 $$The correct calculation shows a premium, but the exact amount calculated here does not match any of the options provided, indicating a mistake in the calculation process. However, the correct approach should involve calculating the present value of the bond's cash flows at the given yield and comparing it to the par value to determine the premium or discount. Given the options and understanding the calculation error, the closest correct approach would indicate a premium, but the exact numbers provided in the options may require recalculating with precise financial formulas or tools.

Nine $2000, 9% Bonds with Interest Payable Semi-Annually and Redeemable